Classification of trisections and the Generalized Property R Conjecture

Meier, Jeffrey; Schirmer, Trent; Zupan, Alexander

doi:10.1090/proc/13105

Classification of trisections and the Generalized Property R Conjecture
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by Jeffrey Meier, Trent Schirmer and Alexander Zupan

Proc. Amer. Math. Soc. 144 (2016), 4983-4997

DOI: https://doi.org/10.1090/proc/13105

Published electronically: May 24, 2016

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Abstract:

We show that the members of a large class of unbalanced four-manifold trisections are standard, and we present a family of trisections that is likely to include non-standard trisections of the four-sphere. As an application, we prove a stable version of the Generalized Property R Conjecture for $c$–component links with tunnel number at most $c$.

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